Transforming the data in order to create a linear relationship between x and y.

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SUMMARY

This discussion focuses on transforming data to establish a linear relationship between variables x and y, specifically using logarithmic transformations. Participants analyze two datasets: one concerning algal cell volume and the other regarding the vapor pressure of B-trimethyl-borazole. Key tasks include plotting the data, determining the appropriateness of logarithmic transformation, calculating the sample correlation coefficient, and fitting a linear model using the least squares method. The discussion highlights the importance of data transformation in achieving linearity for regression analysis.

PREREQUISITES
  • Understanding of logarithmic transformations in data analysis
  • Familiarity with correlation coefficients and their interpretation
  • Knowledge of least squares regression techniques
  • Basic skills in plotting data using software tools like Excel or Python's Matplotlib
NEXT STEPS
  • Learn how to perform logarithmic transformations in data analysis
  • Study the calculation and interpretation of correlation coefficients
  • Explore least squares regression methods in statistical software
  • Investigate various data transformation techniques to achieve linearity
USEFUL FOR

Data analysts, statisticians, and researchers involved in regression analysis and data transformation techniques will benefit from this discussion.

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Homework Statement


A Fisher presents the following data, which give the logarithm to the base 10 of the volume occupied by algal cells on successive days, taken over a period for which the relative growth rate is approximately constant.

Day 1 = 3.592, Day 2 = 3.823, Day 3 = 4.174, Day 4 = 4.532, Day 5 = 4.956, Day 6 = 5.163, Day 7 = 5.495 Day 8 = 5.602, Day 9 = 6.087

Plot y against x. Do you think that the logarithmic transformation is appropriate? If so, why? Calculate and interpret the sample co-relation coefficient . By the method of least squares, fit log = alpha + betax to the n = 9 data points.

The Attempt at a Solution



I don't know what they mean by "transformation is appropriate". What am I supposed to do here? I also don't get what they want me to do with the calculation. Is X the n here? Plug in the values and then calculate it?

Homework Statement



Tukey discusses the relationship between the vapor pressure of B-trimethyl -borazole ( ym in millimeters of mercury) and temperature ( x, in C )

X= 13 y= 2.9 X=56.1 y=51.4 (It's a list with 4 columns. 8 rows ))
X=19.5 y= 5.1 X64.4 y=74.5

Plot y against x. How can we straighten this plot? Try various transformations.

The Attempt at a Solution



Ok, straighten what, how? To it's a straight horizontal line? so I have to compare the X and Y values and find a pattern ? Like, X=4 y=2.. then just use square root for all the y values?
 
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have you plotted you plotted the data? if so what do you see?
 

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